Question

5 find the value of \\( \angle 1 \\).

Explanation:

Step1: Find the adjacent angle of \(152^{\circ}\)

The sum of adjacent angles on a straight line is \(180^{\circ}\). Let the adjacent angle be \(x\), then \(x = 180^{\circ}- 152^{\circ}=28^{\circ}\)

Step2: Use the angle - sum property of a triangle

The sum of angles in a triangle is \(180^{\circ}\). Let \(\angle1=y\), we know one angle is \(x = 28^{\circ}\) and another is \(115^{\circ}\). Then \(y+28^{\circ}+115^{\circ}=180^{\circ}\)

$$y=180^{\circ}-(28^{\circ}+115^{\circ})$$

$$y = 180^{\circ}-143^{\circ}$$

$$y=37^{\circ}$$

Answer:

B. \(37^{\circ}\)